Question 1

In regression analysis:

Accepted Answer

In regression analysis, the core idea is that one variable (the dependent variable) is believed to be influenced by one or more other variables (the independent variables). This does not require the independent variable to be categorical, nor does it imply that the variables must not be correlated. In fact, correlation is essential for regression analysis. The direction of influence is from the independent variable to the dependent variable, not the other way around.

Question 2

If r = .84, the coefficient of determination is equal to:

Accepted Answer

The coefficient of determination is calculated as the square of the correlation coefficient (r). Therefore, if r = .84, the coefficient of determination is .84^2 = .7056, which rounds to .71.

Question 3

When the points in a scatter plot cluster closely around the regression line, the correlation Can be said to be:

Accepted Answer

When points in a scatter plot cluster closely around the regression line, it indicates a strong correlation between the variables, meaning changes in one variable are closely related to changes in the other.

Question 4

The coefficient of determination explains:

Accepted Answer

The coefficient of determination, often denoted as R^2, quantifies the proportion of the variance in the dependent variable (Y) that is predictable from the independent variable(s) (X). It essentially measures how well the regression predictions approximate the real data points.

Question 5

If a = 8 and b = 3, what would be the predicted outcome (Ŷ) for a person with X = 6?

Accepted Answer

Given a = 8 and b = 3, the linear regression equation can be written as Ŷ = a + bX. Substituting the given values, we get Ŷ = 8 + 3(6) = 8 + 18 = 26.

Question 6

Which of the following is NOT a component of the regression equation?

Accepted Answer

The regression equation typically includes the Y-intercept, slope, and error term to model the relationship between variables. The standard deviation is not a component of the regression equation itself but is used in statistical analysis to measure the dispersion of a dataset.

Question 7

In regression analysis, Y is generally considered the __________ variable.

Accepted Answer

The answer of In regression analysis, Y is generally considered...

Question 8

The mathematical equation for a regression line is typically written:

Accepted Answer

The answer of The mathematical equation for a regression line...

Question 9

If the regression line is drawn accurately, the location where it crosses the Y axis is known As:

Accepted Answer

The Y-intercept is the point where the regression line crosses the Y-axis, indicating the value of the dependent variable when the independent variable is zero.

Question 10

If a = 3 and b = 5, a person scoring X = 8 would be predicted to have a Ŷ score of:

Accepted Answer

The answer of If a = 3 and b =...

Question 11

=

Accepted Answer

The answer of  =
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Question 12

Regression analysis creates a mathematical function which predicts the value of the __________ on the basis of the __________.

Accepted Answer

Regression analysis predicts the value of the dependent variable based on the independent variable(s).

Question 13

The square of Pearson's r (r2) is known as the:

Accepted Answer

The square of Pearson's r (r^2) is known as the coefficient of determination, which measures the proportion of variance in the dependent variable that can be predicted from the independent variable.

Question 14

The coefficient of non-determination explains:

Accepted Answer

The coefficient of non-determination explains the proportion of variance in the dependent variable (Y) that cannot be explained by the independent variable(s) (X), essentially the variance in Y that is not accounted for by the model.

Question 15

The difference between the observed points and the regression line points is equal to:

Accepted Answer

The difference between the observed points and the regression line points is referred to as the error term. This represents the amount by which the actual data points deviate from the predicted values on the regression line.

Question 16

.37, the coefficient of non-determination is equal to:

Accepted Answer

The answer of  .37, the coefficient of non-determination is...

Question 17

In a regression equation, the slope accounts for:

Accepted Answer

The slope in a regression equation represents the amount of change in the dependent variable (Y) for each unit change in the independent variable (X).

Question 18

In a regression equation, b refers to:

Accepted Answer

The answer of In a regression equation, b refers to:
...

Question 19

The variable being predicted in a regression analysis is called the:

Accepted Answer

In regression analysis, the variable being predicted is referred to as the dependent variable because its value depends on the values of one or more independent variables.

Question 20

Which of the following is NOT a requirement for regression analysis?

Accepted Answer

All the options listed (interval data, straight line relationship, and random sampling) are indeed requirements for regression analysis.

Quiz 11: Regression Analysis